Hardwire a battery charger?

The plugs you saw were probably for a block heater, a gadget that is installed by cutting the bottom radiator hose and inserting inline to warm the engine coolant. I can't see how leaving a battery charger hooked to the battery all the time would make problems as long as it's mounted securely and the connections are solid. Maybe one of those solar chargers you plug into the cigarette lighter and leave on the dashboard where the sun can get at it would work.

I have a battery tender installed as you've described. It's not a charger so much as a device to maintain the desired voltage. It is hard-wired and the mains plug extends (for my convenience) to the area near the wiper motor pivots. It's possible to overcharge a battery using a standard charger, but not possible when using a battery tender. Your description of use appears to prevent that problem.

Having learned that I can overlook the power cord connection, I also draped the extension wire over one of the wing mirrors. Even better results are to be gained by placing it through or near your door handle!

Consider to install your device in a sheltered area in the engine bay, as most are not designed to be used while exposed to weather and also may be damaged if in airflow which contains precipitation. You may consider to add a shield of some sort, but ensure airflow for cooling.

Normal car battery chargers are plastic or metal boxes, and aren't really rated for the temperatures of the environment under-hood/bonnet.

While you could mount the charger inside a waterproofed and insulated box, its really a short term solution.

Instead, check your battery for a date code, or find out how old it is another way. 5 years used to be considered "normal" life for a battery, now with more modern smaller batteries they tend to die after 3~4. If your battery is older than 5 years just replace it with a new one

The charger you have might be vampiric, draining a small amount of starter battery if the mains supply is not there. Check that with a voltmeter, with the charger connected but not powered, every 24 hours for a few days.

You can also find ways to keep your car more protected too - I can't fathom people who store their vehicles in the driveway outside a perfectly good garage which is filled with not-cars. If you don't have access to a garage or even a car port then my apologies.